The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  X  1 X^2  1  1  1  1  0  1  1 X^2+X  1  1  X  1  0  1  1  1  X  1  1  1  0  1  1 X^2+X  X  1 X^2+X  1  1  0  1 X^2+X  1  1 X^2  X  1  1  1  0  1  1  1  1  1  X X^2  1  1  1  X  1  1  1  0 X^2  1  1  1  1  0  1  X  1  1  X X^2  1  1  1  1  1  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1  1  0 X^2+X+1 X^2 X^2+X+1  1  X  1  1  X X^2+1  1 X+1  1 X^2  1 X^2+X+1  1  X X^2 X^2+X+1  1  X  1  1  1 X^2  1 X^2+1  X  1 X^2  1 X^2+X X+1  1  1  1  X X^2  1 X+1 X^2+X+1  1  0 X^2+X+1  1 X^2 X^2+X X^2 X^2+X+1  X X+1  X  1  1  X  0  0 X^2+X+1 X^2+X  0  0  1 X^2+X  1  0 X^2  1 X^2+X  0  0 X+1  0
 0  0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X  X X^2  X X^2  X  X X^2 X^2  X  X  0 X^2  0 X^2+X X^2  X  0  X X^2+X X^2+X  X X^2+X X^2+X  0 X^2 X^2 X^2 X^2+X X^2  X  0  X  0 X^2+X  0  0  0 X^2+X  0  X  X  X  0 X^2 X^2+X X^2+X  0 X^2 X^2+X  X X^2 X^2+X  0 X^2+X X^2 X^2  0  X  X X^2  0 X^2+X X^2  X X^2+X  0 X^2 X^2+X  X  X  0  X X^2+X X^2+X X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0
 0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+30x^74+112x^75+157x^76+222x^77+344x^78+552x^79+640x^80+756x^81+1035x^82+1130x^83+1267x^84+1310x^85+1342x^86+1356x^87+1318x^88+1188x^89+953x^90+712x^91+554x^92+518x^93+299x^94+196x^95+124x^96+88x^97+63x^98+30x^99+24x^100+14x^101+20x^102+8x^103+4x^104+5x^106+5x^108+3x^110+1x^112+2x^114+1x^116

The gray image is a linear code over GF(2) with n=344, k=14 and d=148.
This code was found by Heurico 1.16 in 22.5 seconds.